Equation 677 Database

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Magma 2174da12f82f…

magma 2174da12f82f
Size
381
Isomorphism class hash
2174da12f82f03842ceb73fc52f227f5ac2d0f993ec74b216eca3a8779a60555
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:50:40
Display reorder
380,79,224,74,89,94,84,219,69,64,54,59,49,199,189,194,214,204,209,159,164,169,174,179,184,324,325,326,327,328,329,43,44,229,99,104,109,124,114,119,234,36,37,42,294,41,39,40,38,264,254,259,249,239,244,134,138,129,149,154,144,299,289,284,274,279,269,369,349,334,354,379,339,344,359,374,363,78,223,73,88,93,83,218,68,63,50,55,48,197,187,192,213,203,208,155,162,166,170,176,181,305,303,304,302,301,300,34,35,228,98,103,108,123,110,115,233,25,26,31,293,30,28,29,27,263,253,258,248,238,243,133,137,128,148,153,143,298,288,283,273,278,268,368,348,333,353,378,338,343,358,373,364,77,222,72,87,92,82,217,67,62,53,58,47,198,188,193,212,202,207,156,160,165,173,175,180,307,308,306,310,311,309,32,33,227,97,102,107,121,111,116,231,2,3,14,290,13,11,12,10,261,250,255,246,235,241,130,136,125,147,152,140,297,287,282,271,275,266,365,347,332,351,376,337,342,356,371,362,75,220,71,86,91,81,216,65,60,51,56,45,196,186,191,211,201,206,157,161,167,171,177,182,315,316,317,312,313,314,1,0,226,95,100,105,120,112,117,230,8,9,7,291,15,4,5,6,260,251,256,245,236,240,132,139,127,146,150,141,296,286,280,270,276,265,366,346,331,350,375,336,340,355,370,361,76,221,70,85,90,80,215,66,61,52,57,46,195,185,190,210,200,205,158,163,168,172,178,183,323,321,322,320,318,319,23,24,225,96,101,106,122,113,118,232,16,17,22,292,21,19,20,18,262,252,257,247,237,242,131,135,126,145,151,142,295,285,281,272,277,267,367,345,330,352,377,335,341,357,372,360 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#fac090d670a9c14492c148fae382a21bad3e48687c67df8555101af0e65e1711, M = {76} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:50:41 · history